Eta-Adjoint Based 4DVAR

Dusanka Zupanski and Milija Zupanski

This advanced assimilation method uses the
adjoint of the Eta Model in the process of deriving initial conditions
which produce the smallest forecast error. A complete 4D-VAR system has
been constructed based on the Eta model adjoint with advanced
pre-conditioning and minimization techniques such that a convergent
solution is attainable in only a few iterations. Recently, efforts have
found that with no loss of accuracy some aspects of the 4DVAR can be
performed at lower resolution and the treatment of the error covariance
can be approximated. Because of the expense of the 4DVAR method, this
efficiency is absolutely paramount. An updated version of NCEP's 4DVAR
system is now available and includes the updated physical processes and
corresponding adjoint model (excluding radiation & cloud).

During 1998,
testing of the new system was curtailed due to funding cuts and lack of
computer resources. The plan to perform a three-way comparison with OI
based EDAS and the 3DVAR based EDAS had to be canceled. Fortunately, a
two week parallel test of the mixed resolution 4DVAR system was
conducted in late January 1999.

Major characteristics of the new 4DVAR
system are: (1) minimization space is defined in coarse resolution, (2)
only NONLINEAR models used in forecast, (3) only COARSE resolution
adjoint model used, (4) 1-hour observational window, (5) observational
operator is same as in the regional 3DVAR system, (6) forecast model
used as a weak constraint (model error), (7) lateral boundary conditions
are adjusted, and (8) background and model error covariances are
anisotropic and non-homogeneous. The defined coarse resolution was
160km/38lyrs and the fine resolution was 80km/38lyrs. Only 10
minimization iterations were performed: 7 in coarse, followed by 3
iterations using fine resolution eta model.

The results indicate an
improvement over 3DVAR for longer forecast periods (36-48 h) while the
short-term forecasts (0-24 h) were worse than 3DVAR forecasts, measured
by observational RMS errors. A probable improvement would be by
performing a few more minimization iterations (10 were not sufficient
for convergence). An improvement over these 4DVAR results was noted
when, after completing the 4DVAR assimilation, an additional 3DVAR was
performed at t=0. Then, short-term forecast errors were greatly
improved, still leaving the long-term forecasts virtually unchanged (and
better than 3DVAR alone). Future experiments will make use of other
available continuous observational data sources collected by during
these real-time experiments for subsequent running / testing in
retrospective mode.